Sign In
Functions are named based on which algebraic expressions they contain.
radical function
We are asked to complete the given sentence.
A ? is a function that contains a radical expression with the independent variable in the radicand. |
Functions can contain many types of algebraic expressions and can be named based on which expressions they contain. Let's take a look at some of the different types of functions and which expressions they contain.
Name of the Function | Example | Characteristic of the Function |
---|---|---|
Linear Function | f(x)=3x+4 | The highest exponent of the independent variable is 1. |
Quadratic Function | g(x)=x2+5x+7 | The highest exponent of the independent variable is 2. |
Cubic Function | k(x)=x3+5x2+6x−9 | The highest exponent of the independent variable is 3. |
Exponential Function | ℓ(x)=7x | The function contains a variable exponent. |
Absolute Value Function | t(x)=∣x2−4x∣ | The function contains the absolute value of a variable expression. |
Square Root Function | m(x)=3x+9 | The function contains a radical expression with an index of 2 and the independent variable in the radicand. |
Cube Root Function | n(x)=3x−8 | The function contains a radical expression with an index of 3 and the independent variable in the radicand. |
Notice that both the square root function and the cube root function contain radical expressions with the independent variable x in the radicand. Since the common characteristic between them is that they include variable expressions under a radical sign, they are also known as radical functions. Knowing this, we can complete our sentence.
A radical function is a function that contains a radical expression with the independent variable in the radicand. |